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292 lines
11 KiB
Python
292 lines
11 KiB
Python
#!/usr/bin/python
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# coding:utf8
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'''
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Create by ApacheCN-小瑶
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Date from 2017-02-27
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'''
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from numpy import *
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import matplotlib.pylab as plt
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def loadDataSet(fileName): #解析以tab键分隔的文件中的浮点数
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numFeat = len(open(fileName).readline().split('\t')) - 1 #获得每一行的输入数据，最后一个代表真实值
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dataMat = []; labelMat = []
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fr = open(fileName)
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for line in fr.readlines(): #读取每一行
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lineArr =[]
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curLine = line.strip().split('\t') #删除一行中以tab分隔的数据前后的空白符号
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for i in range(numFeat): #从0到2，不包括2
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lineArr.append(float(curLine[i]))#将数据添加到lineArr List中，每一行数据测试数据组成一个行向量
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dataMat.append(lineArr) #将测试数据的输入数据部分存储到dataMat矩阵中
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labelMat.append(float(curLine[-1]))#将每一行的最后一个数据，即真实的目标变量存储到labelMat矩阵中
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return dataMat,labelMat
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def standRegres(xArr,yArr): #线性回归
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xMat = mat(xArr); yMat = mat(yArr).T #mat()函数将xArr，yArr转换为矩阵
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xTx = xMat.T*xMat #矩阵乘法的条件是左矩阵的列数等于右矩阵的行数
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if linalg.det(xTx) == 0.0: #因为要用到xTx的逆矩阵，所以事先需要确定计算得到的xTx是否可逆，条件是矩阵的行列式不为0
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print ("This matrix is singular, cannot do inverse")
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return
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# 最小二乘法
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# http://www.apache.wiki/pages/viewpage.action?pageId=5505133
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ws = xTx.I * (xMat.T*yMat) #书中的公式，求得w的最优解
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return ws
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def lwlr(testPoint,xArr,yArr,k=1.0): #局部加权线性回归
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xMat = mat(xArr); yMat = mat(yArr).T
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m = shape(xMat)[0] #获得xMat矩阵的行数
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weights = mat(eye((m))) #eye()返回一个对角线元素为1，其他元素为0的二维数组，创建权重矩阵
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for j in range(m): #下面两行创建权重矩阵
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diffMat = testPoint - xMat[j,:] #遍历数据集，计算每个样本点对应的权重值
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weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))#k控制衰减的速度
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xTx = xMat.T * (weights * xMat)
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if linalg.det(xTx) == 0.0:
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print ("This matrix is singular, cannot do inverse")
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return
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ws = xTx.I * (xMat.T * (weights * yMat)) #计算出回归系数的一个估计
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return testPoint * ws
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def lwlrTest(testArr,xArr,yArr,k=1.0): #循环所有的数据点，并将lwlr运用于所有的数据点
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m = shape(testArr)[0]
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yHat = zeros(m)
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for i in range(m):
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yHat[i] = lwlr(testArr[i],xArr,yArr,k)
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return yHat
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def lwlrTestPlot(xArr,yArr,k=1.0): #首先将 X 排序，其余的都与lwlrTest相同，这样更容易绘图
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yHat = zeros(shape(yArr))
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xCopy = mat(xArr)
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xCopy.sort(0)
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for i in range(shape(xArr)[0]):
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yHat[i] = lwlr(xCopy[i],xArr,yArr,k)
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return yHat,xCopy
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def rssError(yArr,yHatArr): #yArr 和 yHatArr 两者都需要是数组
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return ((yArr-yHatArr)**2).sum()
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def ridgeRegres(xMat,yMat,lam=0.2): #岭回归
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xTx = xMat.T*xMat
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denom = xTx + eye(shape(xMat)[1])*lam #按照书上的公式计算计算回归系数
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if linalg.det(denom) == 0.0: #检查行列式是否为零，即矩阵是否可逆
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print ("This matrix is singular, cannot do inverse")
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return
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ws = denom.I * (xMat.T*yMat)
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return ws
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def ridgeTest(xArr,yArr):
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xMat = mat(xArr); yMat=mat(yArr).T
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yMean = mean(yMat,0) #计算Y均值
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yMat = yMat - yMean #Y的所有的特征减去均值
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#标准化 x
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xMeans = mean(xMat,0) #X计算平均值
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xVar = var(xMat,0) #然后计算 X的方差
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xMat = (xMat - xMeans)/xVar
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numTestPts = 30
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wMat = zeros((numTestPts,shape(xMat)[1]))#创建30 * m 的全部数据为0 的矩阵
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for i in range(numTestPts):
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ws = ridgeRegres(xMat,yMat,exp(i-10))#exp返回e^x
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wMat[i,:]=ws.T
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return wMat
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def regularize(xMat):#按列进行规范化
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inMat = xMat.copy()
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inMeans = mean(inMat,0) #计算平均值然后减去它
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inVar = var(inMat,0) #计算除以Xi的方差
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inMat = (inMat - inMeans)/inVar
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return inMat
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def stageWise(xArr,yArr,eps=0.01,numIt=100):
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xMat = mat(xArr); yMat=mat(yArr).T
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yMean = mean(yMat,0)
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yMat = yMat - yMean #也可以规则化ys但会得到更小的coef
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xMat = regularize(xMat)
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m,n=shape(xMat)
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#returnMat = zeros((numIt,n)) #测试代码删除
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ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()
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for i in range(numIt):
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print (ws.T)
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lowestError = inf;
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for j in range(n):
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for sign in [-1,1]:
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wsTest = ws.copy()
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wsTest[j] += eps*sign
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yTest = xMat*wsTest
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rssE = rssError(yMat.A,yTest.A)
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if rssE < lowestError:
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lowestError = rssE
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wsMax = wsTest
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ws = wsMax.copy()
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#returnMat[i,:]=ws.T
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#return returnMat
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#def scrapePage(inFile,outFile,yr,numPce,origPrc):
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# from BeautifulSoup import BeautifulSoup
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# fr = open(inFile); fw=open(outFile,'a') #a is append mode writing
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# soup = BeautifulSoup(fr.read())
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# i=1
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# currentRow = soup.findAll('table', r="%d" % i)
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# while(len(currentRow)!=0):
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# title = currentRow[0].findAll('a')[1].text
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# lwrTitle = title.lower()
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# if (lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1):
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# newFlag = 1.0
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# else:
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# newFlag = 0.0
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# soldUnicde = currentRow[0].findAll('td')[3].findAll('span')
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# if len(soldUnicde)==0:
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# print "item #%d did not sell" % i
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# else:
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# soldPrice = currentRow[0].findAll('td')[4]
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# priceStr = soldPrice.text
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# priceStr = priceStr.replace('$','') #strips out $
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# priceStr = priceStr.replace(',','') #strips out ,
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# if len(soldPrice)>1:
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# priceStr = priceStr.replace('Free shipping', '') #strips out Free Shipping
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# print "%s\t%d\t%s" % (priceStr,newFlag,title)
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# fw.write("%d\t%d\t%d\t%f\t%s\n" % (yr,numPce,newFlag,origPrc,priceStr))
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# i += 1
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# currentRow = soup.findAll('table', r="%d" % i)
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# fw.close()
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'''
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from time import sleep
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import json
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import urllib2
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def searchForSet(retX, retY, setNum, yr, numPce, origPrc):
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sleep(10)
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myAPIstr = 'AIzaSyD2cR2KFyx12hXu6PFU-wrWot3NXvko8vY'
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searchURL = 'https://www.googleapis.com/shopping/search/v1/public/products?key=%s&country=US&q=lego+%d&alt=json' % (myAPIstr, setNum)
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pg = urllib2.urlopen(searchURL)
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retDict = json.loads(pg.read())
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for i in range(len(retDict['items'])):
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try:
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currItem = retDict['items'][i]
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if currItem['product']['condition'] == 'new':
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newFlag = 1
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else: newFlag = 0
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listOfInv = currItem['product']['inventories']
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for item in listOfInv:
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sellingPrice = item['price']
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if sellingPrice > origPrc * 0.5:
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print ("%d\t%d\t%d\t%f\t%f" % (yr,numPce,newFlag,origPrc, sellingPrice))
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retX.append([yr, numPce, newFlag, origPrc])
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retY.append(sellingPrice)
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except: print ('problem with item %d' % i)
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def setDataCollect(retX, retY):
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searchForSet(retX, retY, 8288, 2006, 800, 49.99)
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searchForSet(retX, retY, 10030, 2002, 3096, 269.99)
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searchForSet(retX, retY, 10179, 2007, 5195, 499.99)
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searchForSet(retX, retY, 10181, 2007, 3428, 199.99)
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searchForSet(retX, retY, 10189, 2008, 5922, 299.99)
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searchForSet(retX, retY, 10196, 2009, 3263, 249.99)
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def crossValidation(xArr,yArr,numVal=10):
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m = len(yArr)
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indexList = range(m)
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errorMat = zeros((numVal,30))#create error mat 30columns numVal rows创建error mat 30columns numVal 行
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for i in range(numVal):
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trainX=[]; trainY=[]
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testX = []; testY = []
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random.shuffle(indexList)
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for j in range(m):#create training set based on first 90% of values in indexList
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#基于indexList中的前90%的值创建训练集
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if j < m*0.9:
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trainX.append(xArr[indexList[j]])
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trainY.append(yArr[indexList[j]])
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else:
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testX.append(xArr[indexList[j]])
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testY.append(yArr[indexList[j]])
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wMat = ridgeTest(trainX,trainY) #get 30 weight vectors from ridge
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for k in range(30):#loop over all of the ridge estimates
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matTestX = mat(testX); matTrainX=mat(trainX)
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meanTrain = mean(matTrainX,0)
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varTrain = var(matTrainX,0)
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matTestX = (matTestX-meanTrain)/varTrain #regularize test with training params
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yEst = matTestX * mat(wMat[k,:]).T + mean(trainY)#test ridge results and store
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errorMat[i,k]=rssError(yEst.T.A,array(testY))
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#print errorMat[i,k]
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meanErrors = mean(errorMat,0)#calc avg performance of the different ridge weight vectors
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minMean = float(min(meanErrors))
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bestWeights = wMat[nonzero(meanErrors==minMean)]
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#can unregularize to get model
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#when we regularized we wrote Xreg = (x-meanX)/var(x)
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#we can now write in terms of x not Xreg: x*w/var(x) - meanX/var(x) +meanY
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xMat = mat(xArr); yMat=mat(yArr).T
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meanX = mean(xMat,0); varX = var(xMat,0)
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unReg = bestWeights/varX
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print ("the best model from Ridge Regression is:\n",unReg)
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print ("with constant term: ",-1*sum(multiply(meanX,unReg)) + mean(yMat))
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'''
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#test for standRegression
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def regression1():
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xArr, yArr = loadDataSet("testData/Regression_data.txt")
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xMat = mat(xArr)
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yMat = mat(yArr)
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ws = standRegres(xArr, yArr)
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fig = plt.figure()
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ax = fig.add_subplot(111) #add_subplot(349)函数的参数的意思是，将画布分成3行4列图像画在从左到右从上到下第9块
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ax.scatter(xMat[:, 1].flatten(), yMat.T[:, 0].flatten().A[0]) #scatter 的x是xMat中的第二列，y是yMat的第一列
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xCopy = xMat.copy()
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xCopy.sort(0)
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yHat = xCopy * ws
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ax.plot(xCopy[:, 1], yHat)
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plt.show()
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#test for LWLR
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def regression2():
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xArr, yArr = loadDataSet("testData/Regression_data.txt")
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yHat = lwlrTest(xArr, xArr, yArr, 0.003)
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xMat = mat(xArr)
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srtInd = xMat[:,1].argsort(0) #argsort()函数是将x中的元素从小到大排列，提取其对应的index(索引)，然后输出
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xSort=xMat[srtInd][:,0,:]
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fig = plt.figure()
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ax = fig.add_subplot(111)
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ax.plot(xSort[:,1], yHat[srtInd])
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ax.scatter(xMat[:,1].flatten().A[0], mat(yArr).T.flatten().A[0] , s=2, c='red')
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plt.show()
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#test for ridgeRegression
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def regression3():
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abX,abY = loadDataSet("testData/Regression_abalone.txt")
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ridgeWeights = ridgeTest(abX, abY)
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fig = plt.figure()
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ax = fig.add_subplot(111)
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ax.plot(ridgeWeights)
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plt.show()
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#test for stageWise
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def regression4():
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xArr,yArr=loadDataSet("testData/Regression_abalone.txt")
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stageWise(xArr,yArr,0.01,200)
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xMat = mat(xArr)
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yMat = mat(yArr).T
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xMat = regularize(xMat)
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yM = mean(yMat,0)
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yMat = yMat - yM
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weights = standRegres(xMat, yMat.T)
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print (weights.T)
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if __name__ == "__main__":
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# regression1()
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regression2()
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# regression3()
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# regression4() |